How to tweak verts while in Anotate tool active?
They use right-click for selection in the video. It's a preference setting: Preferences... → Keymap → Preferences section → Select with Mouse Button left / right.
With right-click for selection you can use the Annotation tool with the left mouse button, and drag vertices around with the right mouse button. In Selection mode, new vertices can be extruded with Ctrl + left-click. The context menu is opened with the W key.
Video: Right Click Select - Blender 2.80 Fundamentals